Continuum contribution

Tanner and Thakkar (12) have obtained ai,(oo) = 3.66325789. Then it is possible to deduce the continuum contribution of, = 0.8367, i.e. about 18.6% of the total electronic polarizability. 

In order to demonstrate the efficiency of the g f) function in the calculation of the polarizability. Rerat et al. (13) have carried out the calculation of the polarizability for the ground state of the hydrogen atom. This computation has been made with aff N)) and without ai, N)) the dipolar factor, versus the number of the spectral l n) states involved in the calculation. The convergence of such series aif N) and ai (N) leads to discrete values of 4.4018 and 3.6632 (i.e. the result of Tarmer and Thakkar) corresponding respectively to 97.8% and 81.4% of the exact value. This result illustrates the fact that a large part of the continuum contribution is simulated through the use of the dipolar factor. Moreover the convergence of the series aif N) is faster as we can see on table 1. 

A typical convergence study with the size of the continuum contributions is shown in Table 3 for ls2p P2-state. These corrections are of the order of 23% for the scalar part of polarizabihty and only of the order of 3% for the tensor part. The magnitude of the electric held and the energy separation at anticrossing 0 X 0 are F = 632.96 kV/cm and AE = 30084 MHz, respectively. 

We have calculated the second- and fourth-order dipole susceptibilities of an excited helium atom. Numerical results have been obtained for the ls2p Pq-and ls2p f2-states of helium. For the accurate calculations of these quantities we have used the model potential method. The interaction of the helium atoms with the external electric held F is treated as a perturbation to the second- and to the fourth orders. The simple analytical expressions have been derived which can be used to estimate of the second- and higher-order matrix elements. The present set of numerical data, which is based on the Green function method, has smaller estimated uncertainties in ones than previous works. This method is developed to high-order of the perturbation theory and it is shown specihcally that the continuum contribution is surprisingly large and corresponds about 23% for the scalar part of polarizability. 

The errors apparently are not due to any corrections that would come in for each pair term e,p in Eq. (167), such as continuum contributions to London s formula. These would also be proportional to X nt, and give similar correction factors for He and H2 as for Ne, A, etc. 

Figure 14. As Figure 13, but for mercury vapor. Owing to ground state configuration interaction the L2 and L3 spectra converge to two separate continua 6s Sq and 6p Thus the broken curve for the continuum contribution is also a sum of two arctan curves. (From Ref. 53.)... 

Figure 6. Cross section profiles relative to the 6Hy, 6Gg and lOHg orbitals of Cgp (solid lines). Final continuum contributions Tig(jy) (.), T2g(2u) ( —). Gg(u) (—.) Hg( ) (-------).

More extensive calculations have been performed taking into account both pathways simultaneously. The resulting coherent sum of the continuum contributions is shown in the upper curve of Fig. 3.27c, together with the interference term... 

Laser-induced fluorescence also offers the possibility of looking at the solvation structure in its isolated form, that is, short-range order without the continuum contribution. This has attracted keen interest in supersonic molecular beam studies of van der Waals complexes (27-28). The successive additions of n solvating molecules B form a solvated species AB. Spectral shifts and lineshape changes in the absorption of A as it becomes AB, or in the laser-induced fluorescence decay of those consecutively... 

Our Br7 image reveals filamentary structure that traces the limbs of the bipolar cavities out to 80" from S106IR. The lobe interiors have a knotty appearance, hi contrast, the surface bri tness in the continuum image is more uniformly distributed. Comparison of the intensities in the on-line/ofif-line pair indicates that the continuum contributes typically 20% of the flux within the Fabry-Perot filter passband. 

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